[General] meaning of "the spare change of myself that no one yet had pocketed" and "arch"

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meaning of "the spare change of myself that no one yet had pocketed" and "arch"

I'm reading The Muse by Jessie Burton and was confused about these two sentences.

1. "Cynth once told me that I looked better in profile, and I said that made me sound like I was a coin. But now it makes me wonder about my two sides, the arch impression I probably gave Pamela, the spare change of myself that no one yet had pocketed."

Does "the spare change of myself that no one yet had pocketed" mean an aspect which no one had yet discovered about the narrator? I can't pinpoint the exact meaning.

2. The narrator's new boss asked her if people in her country, Trinidad, speak French. She gave the answer: "Only a few of our forebears were indoors, speaking with the French," but "dreaded that my history lesson was too much, too arch."

Does "arch impression" in the first sentence mean an overall impression? And does "too arch" in the two sentence means too general or too abstract?